Recent advances in the study of convergence to equilibrium for the Becker-Doring equations.

The Becker-Döring equations are a fundamental set of equations that describe the kinetics of first order phase transition, and are applicable to a wide variety of phenomena such as crystallisation, vapour condensation and aggregation of lipids.
While the equations can be traced back to a model from 1935, a rigorous systematic study of them, and the long time behaviour of their solutions, only appeared around the 80’s in works by Ball, Carr and Penrose.
In our talk we will focus on the natural setting of the equations where the existence of, and convergence to, a state of equilibrium have been shown. We will use the so-called entropy method to find a quantitative estimation for the rate of this convergence, and see how this relates to the question of a uniform in time bounds of the moments of the solution – another new result we shall discuss.
This talk is based on a couple of papers that are a joint work with José Cañizo and Bertrand Lods.